# SPECTRAL THEORY IN HILBERT SPACES

Lecturer: Prof. Dr. S. Warzel Exercises: Dr. Huajie Chen## Time and location:

Lectures: Thursday, 8:30 - 10:00, MI Hörsaal 3Friday, 12:00 - 13:30, Seminarraum 03.08.011

**On Thursday 16.5. the class is cancelled.**(We will be doing overtime the previous Fridays). Exercise classes: Tuesday, 14:15-15:45, Seminarraum 01.07.023

First exercise class: 30.4.

**On Tuesday 11.6. the exercise class is cancelled.**There will be an additional exercise class on Thursday 11.7. from 8:30 - 10:00, MI Hörsaal 3

**On On Thursday 11.7. the class is cancelled and there will be an exercise session instead.**

## Content:

- Spectral theory of compact operators
- Unbounded linear operators
- Spectral theorem for self-adjoint operators
- Formalism of quantum mechanics

## Literature:

- Handwritten notes (will be provided during the course, see below)
- N. Akhiezer, I. Glazman, Theory of linear operators in Hilbert space, Dover 1993.
- M. Reed, B. Simon, Methods of Modern Mathematical Physics, I, Functional Analysis, Academic Press, 1980.
- J. Weidmann, Linear Operators in Hibert spaces, Springer 1980.

## Summary of the lecture:

- Week1.pdf
- Week2.pdf
- Week3.pdf
- Week4.pdf
- Week5.pdf
- Week6.pdf
- Week7.pdf
- Week8.pdf
- Week9.pdf
- Week10.pdf
- Week11.pdf
- Week12.pdf
- Week13.pdf
- Week14.pdf

## Exercise sheets:

- Exercise1.pdf Solutions.pdf
- Exercise2.pdf Solutions.pdf
- Exercise3.pdf Solutions.pdf
- Exercise4.pdf Solutions.pdf
- Exercise5.pdf Solutions.pdf
- Exercise6.pdf Solutions.pdf
- Exercise7.pdf Solutions.pdf
- Exercise8.pdf Solutions.pdf
- Exercise9.pdf Solutions.pdf
- Exercise10.pdf Solutions.pdf
- Exercise11.pdf Solutions.pdf

## Exam:

There will be a written exam of 90min on**Monday, 29.7. at 9:00 in Seminarraum 00.07.014.**You can bring one A4 sized paper with hand written notes on both sides. No other auxiliary tools are allowed. Klausureinsicht: 30.7., 14:00-15:00 in Glaskasten 03.08.022B Nachholklausur:

**Wednesday, 02.10. at 14:30-16:00 in Seminarraum 02.08.020.**(Under the same conditions as the original exam.)